According to the MMBasic documentation the command OPTION SYSTEM I2C the speed can be set to SLOW (100KHz) or FAST (400KHz).
This option using WebMite Ver 6.00.03 on a Pico 2W is set to SLOW.
With the help of a plumbing modification (3 mm rubber washers) to keep the board in place without the back cover I was able to connect a ZOYI ZT-703S oscilloscope multimeter to I2C1 SDA (GP6) and I2C1 SCL (GP7). The following screenshot confirms that the I2C1 clock speed is 10KHz.
Unfortunately I was unable to find this in the documentation.
Digging into the forum and the source code I was able to find why this is has been done. However, while looking at the source code I noticed a few things that I may look into at a later date when I have time available because it should be viable to run at 100 Khz or more. (I have successfully tested I2C at 4MHz (and more) using wirewrap between multiple Pico 1).
One issue I noticed in the code is that every Pico I2C interface is clocked at 10KHz, this does not make sense if this was done because of a communication problem using I2C1 with the keyboard.